Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
924 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#6312 | C2 | semidirect |
| 2. C2×C32×C3⋊Dic3 | C2 | semidirect |
| 3. C33×#67 | C2 | semidirect |
| 4. C3×#6293 | C2 | semidirect |
| 5. C3×#6291 | C2 | semidirect |
| 6. C3×#6289 | C2 | semidirect |
| 7. C3×D3×C3⋊Dic3 | C2 | semidirect |
| 9. #89028 | C3 | direct (N × H) |
| 19. #6312 | C2×C3 | semidirect |
| 26. C2×C3×C3⋊Dic3 | D3 | semidirect |
| 27. C2×C3×C3⋊Dic3 | C2×C3 | semidirect |
| 31. C32×#67 | D3 | semidirect |
| 32. C32×#67 | C2×C3 | semidirect |
| 34. #6293 | C2×C3 | semidirect |
| 35. #6291 | C2×C3 | semidirect |
| 36. #6289 | C2×C3 | semidirect |
| 37. D3×C3⋊Dic3 | C2×C3 | semidirect |
| 81. C34 | #41 | semidirect |
| 91. C2×C3⋊Dic3 | C3×D3 | semidirect |
| 99. C3×#67 | C3×D3 | semidirect |
| 100. C3×#67 | C3⋊D3 | semidirect |
| 190. C33 | #235 | semidirect |
| 191. C33 | #237 | semidirect |
| 192. C33 | C3×#41 | semidirect |
| 208. #67 | C3×C3⋊D3 | semidirect |
| 293. C32 | #3804 | semidirect |
| 294. C32 | C3×#235 | semidirect |
| 295. C32 | C3×#237 | semidirect |
| 296. C32 | #3830 | semidirect |
| 337. C3 | C3×#3804 | semidirect |
| 338. C3 | #89028 | direct (N × H) |
| 339. C3 | C3×#3830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6312 | 2 |
| C2×C32×C3⋊Dic3 | 2 |
| C33×#67 | 2 |
| C3×#6293 | 2 |
| C3×#6291 | 2 |
| C3×#6289 | 2 |
| C3×D3×C3⋊Dic3 | 2 |
| C3×#3830 | 3 |
| #89028 | 3 |
| C3×#3804 | 3 |